Series, Parallel and Domestic Electricity
Series and Parallel Circuits
In a series circuit, all components are in a single continuous loop. This means:
• Current is the same at every point in the circuit — charge is not used up.
• Potential difference is shared between components — the sum of individual voltages equals the supply voltage.
• Total resistance = sum of individual resistances: \(R_{\text{total}} = R_1 + R_2 + R_3\)
• If one component fails, the circuit breaks and all components stop working.
In a parallel circuit, components are on separate branches. This means:
• Potential difference is the same across each branch (and equals the supply voltage).
• Current splits between branches — more current flows through the branch with lower resistance.
• Total resistance is lower than the smallest individual resistance because there are more paths for current.
• If one component fails, the others continue to work. This is why household appliances use parallel wiring.
Series: current the same everywhere; PD shared. Parallel: PD the same across each branch; current shared. Adding resistors in parallel decreases total resistance (more paths available).
Series: Two resistors of 6 Ω and 4 Ω in series: \(R_{\text{total}} = 6 + 4 = 10 \text{ } \Omega\). If the supply is 20 V, the current everywhere is \(I = \frac{V}{R} = \frac{20}{10} = 2 \text{ A}\). The 6 Ω resistor has \(V = 2 \times 6 = 12 \text{ V}\) across it; the 4 Ω resistor has \(V = 2 \times 4 = 8 \text{ V}\). Sum: \(12 + 8 = 20 \text{ V}\) ✓
Parallel: Two 6 Ω resistors in parallel. Each has 12 V across it. Current in each branch: \(I = \frac{12}{6} = 2 \text{ A}\). Total current from supply: \(2 + 2 = 4 \text{ A}\). Effective total resistance: \(R = \frac{12}{4} = 3 \text{ } \Omega\) — lower than either individual resistor.
AC and DC
Scope note: mains electricity, plug wiring and the National Grid are topic P8.2, examined on Physics Paper 2 (F2 / H4). They sit here because they follow on from circuits.
Direct current (DC) flows in one direction only — this is what batteries and solar cells produce. Alternating current (AC) constantly reverses direction. The UK mains supply is AC at a frequency of 50 Hz (50 complete cycles per second) and a voltage of about 230 V. On an oscilloscope trace, AC appears as a sine wave oscillating above and below zero; DC appears as a flat horizontal line.
UK domestic mains: AC at 230 V and 50 Hz. Batteries: DC. AC can have its voltage changed by a transformer; DC cannot. On an oscilloscope trace: AC = wave, DC = flat line.
Mains Wiring and Safety
A UK three-pin plug contains three wires, each with a specific colour and function:
• Live (brown) — carries the AC supply at about 230 V. Always dangerous, even when the appliance is switched off, because it remains connected to the mains supply.
• Neutral (blue) — completes the circuit at approximately 0 V. Current flows in through the live and out through the neutral.
• Earth (green and yellow striped) — a safety wire connected to the metal casing of an appliance. Provides a low-resistance path to earth if a fault causes the casing to become live.
A fuse is always in the live wire. If the current exceeds the fuse rating, the fuse wire melts and breaks the circuit, preventing overheating or fire. The earth wire and fuse work together: if the live wire accidentally touches the metal casing, a surge of current flows through the earth wire, blowing the fuse and cutting the supply. A residual current device (RCD) provides faster protection by detecting any imbalance between live and neutral currents and cutting the circuit within milliseconds.
Appliances with plastic casings (such as hairdryers and power drills) use double insulation. The plastic casing cannot become live because it is an insulator, so there is no risk of the user receiving an electric shock even if the wiring inside develops a fault. These appliances are marked with a double-square symbol and do not require an earth wire. This makes them safe in damp environments where a metal-cased appliance with a faulty earth could be particularly dangerous.
Electrical Power and Energy
Electrical power is the rate of energy transfer. The key equations are:
$$P = V \times I \qquad P = I^2 \times R$$
Where \(P\) is power (W), \(V\) is potential difference (V), \(I\) is current (A), and \(R\) is resistance (Ω). The second equation is useful when voltage is not known. The total energy transferred is:
$$E = P \times t$$
Where \(E\) is energy (J) and \(t\) is time (s). For domestic billing, energy is measured in kilowatt-hours (kWh): one kWh = a 1 kW appliance running for 1 hour. Cost = energy (kWh) × price per kWh.
Power equations: \(P = VI\), \(P = I^2R\). Energy transferred: \(E = Pt\). Domestic energy unit: kilowatt-hour (kWh). Cost (pence) = energy (kWh) × price per unit.
The National Grid
The National Grid transmits electricity from power stations to consumers across the UK. Electricity is transmitted at very high voltages (up to several hundred thousand volts) and correspondingly low currents to minimise energy losses in the cables. Since the power wasted as heat in cables is \(P_{\text{loss}} = I^2 R\), a smaller current dramatically reduces losses — squaring the current means even a small reduction in current makes a large difference.
Step-up transformers at power stations increase voltage (and reduce current) for long-distance transmission. Step-down transformers at local substations reduce the voltage to 230 V for safe household use. Transformers only work with AC because they rely on a changing magnetic field in the core to induce a voltage in the secondary coil; a DC supply would produce a constant field and no induced voltage.